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A096865 Function A062401(x) = phi(sigma(x)) is iterated. Starting with n, a(n) is the smallest term arising in trajectory, either in transient or in terminal cycle.

%I A096865 #14 Nov 18 2017 21:00:17
%S A096865 1,2,2,4,2,4,4,8,9,4,4,12,4,8,8,16,4,16,8,12,16,12,8,16,16,12,16,16,8,
%T A096865 16,16,32,16,16,16,36,16,16,16,16,12,32,12,16,16,16,16,48,36,48,16,32,
%U A096865 16,32,16,32,32,16,16,48,16,32,48,64,16,48,32,36,32,48,16,72,36,36,48
%N A096865 Function A062401(x) = phi(sigma(x)) is iterated. Starting with n, a(n) is the smallest term arising in trajectory, either in transient or in terminal cycle.
%H A096865 Antti Karttunen, <a href="/A096865/b096865.txt">Table of n, a(n) for n = 1..16384</a>
%e A096865 n=255: list={255,144,360,288,[432,480],432,...}, a(255)=144 as a transient term;
%e A096865 n=254: list={254,[128],128,...}, a(254)=128, as a fixed point.
%t A096865 fs[x_] :=EulerPhi[DivisorSigma[1, x]] itef[x_, hos_] :=NestList[fs, x, hos] Table[Min[itef[w, 20]], {w, 1, 256}]
%o A096865 (Scheme) (define (A096865 n) (let loop ((visited (list n)) (m n)) (let ((next (A062401 (car visited)))) (cond ((member next visited) m) (else (loop (cons next visited) (min m next))))))) ;; _Antti Karttunen_, Nov 18 2017
%Y A096865 Cf. A062401, A062402, A095955, A096859, A096860, A096861 (largest term).
%Y A096865 Cf. also A096866.
%K A096865 nonn
%O A096865 1,2
%A A096865 _Labos Elemer_, Jul 21 2004